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\begin{document}
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\title{Finding Ego-centric Communities for Identifying Nodes in a Heterogeneous Network}

% author names and affiliations
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\author{\IEEEauthorblockN{Jhao-Yin Li and Mi-Yen Yeh}
\IEEEauthorblockA{Institute of Information Science, Academia Sinica\\
Taipei, Taiwan 115\\
Email: louisjyli@iis.sinica.edu.tw, miyen@iis.sinica.edu.tw}
\and
\IEEEauthorblockN{Shou-De Lin}
\IEEEauthorblockA{Department of Computer Science and Information Engineering\\
National Taiwan University, Taipei City, Taiwan 10617\\
Email: sdlin@csie.ntu.edu.tw}}

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\section{Introduction}
Given a graph, can we identify a specific node ID by its own related information? It is very important that whenever a node's ID is missing, how can we recover it by means of investigating other nodes and their corresponding structure. In general cases, users have to query out the missing node; however, it is hard to know what kind of query statement is the most efficient to identify the missing node. To avoid wasting time on failure queries, we are in need of an algorithm to produce some efficient query statements to help users quickly retrieve the missing ID.\\
We propose to adopt community detection methods that can extract a ego-centric subgraph from a large network. Those subgraphs can be used as the egos' neighbor information, and may help to identify the ego if needed. Furthermore, they may also be identified with each other in the community. An ego-centric self-identified community is a better query statements than blind search.On the other words, our goal is to extract an ego-centric community community that each node in this community can be uniquely identified. Therefore, if a node ID is missing, we can successfully recover it since the missing node can be uniquely identified.\\
Firstly, we explain how this happens in a homogeneous network. Suppose we have a graph shown as Fig.~\ref{fig:ex1}. If we want to query: \emph{A node that is connected with the node 1}. We can have 2 responses - Node 0, Node 3, and Node 4. In this case, we can hardly determine the node ID we desired since all 3 nodes are fully satisfy the query. However, what if we change the query to: \emph{A node that is connected with the node 2}? , we can definitely get only 1 result, Node 0, which is exactly satisfy the query. Finally, we can make sure that the missing node should be Node 0.\\
\begin{figure}[t]
\centering
\includegraphics[scale=0.5]{fig-ex1.eps}
\caption{A Homogeneous Network}
\vspace*{-3mm}
\label{fig:ex1}
\end{figure}
Moreover, we apply the above concept on heterogeneous networks. If we have a graph shown as Fig.~\ref{fig:ex2}, and we query that: \emph{A circle node that is connected with the node 1}. We can explicitly have 2 responses - Node 0, and Node 3. Note that Node 4 is not a qualified response in this case since it is a square node rather than a circle node. However, we still cannot easily determine the node ID since both nodes are fully satisfy the query. However, if we modify the query to: \emph{A circle node that is connected with the node 2}, we can definitely get a single result, Node 0, which is also exactly satisfy the query. We can infer that the missing node must be Node 0 rather than something else.\\
\begin{figure}[b]
\centering
\includegraphics[scale=0.5]{fig-ex2.eps}
\caption{A Heterogeneous Network}
\vspace*{-3mm}
\label{fig:ex2}
\end{figure}
<<Summarize Our Methods and Findings Here>>\\
This paper has following contributions to the network analysis filed:
\begin{itemize}
\item
It is the first study to address the node identification problem in a large network.
\item
We further extended this problem onto the Heterogeneous Social Networks (HSN).
\item
This work not only formally defined the problem but also set a reasonable evaluation scheme.
\item
We designed a greedy method for finding a self-identified community from each node in a large network.
\item
The experimental results showed that our propose method surpassed several conventional methods.
\end{itemize}

\section{Related Works}
Citation test : ~\cite{citation1} and ~\cite{citation2} and~\cite{citation3}\\
\textbf{Community Detection.}\\
\textbf{Ego-centric Networks.}\\
\textbf{Node Identification.}\\

\section{Methodology}
In this section, we formally describe our research problem and propose definitions as well as related terminologies. In sum, the research problem can be modeled as following:\\
\textbf{Input:} (1) A Heterogeneous Network \emph{H}. (2) A user specified query ego node $N_t$.\\
\textbf{Output:} An ego-centric community based on the ego node $N_t$.\\
\begin{definition}
\textbf{Heterogeneous Network:} A heterogeneous network $H(V, E, T)$ is an undirected attributed graph, where $V$ is a finite set of nodes, $E \subseteq V \times V$ is a finite set of edges, and $T$ is a finite set of types. The type function $T(V) \longrightarrow \{ \{ t_1,...,t_i \} ,t_i \in T, i \geq 1 \} $ maps each vertex into its unique type.\\
\end{definition}
The \emph{Ambiguity} results when more than 2 identities satisfy a certain criteria. For instance, we may ask a question like: "The actors who performed in the Star Wars serious." Such a question may have tens of actors who are qualified for this question, thus the \emph{Ambiguity} of this query is very high. A possible way to measure the \emph{Ambiguity} is to compute their \emph{Entropy}, which is defined as:
\begin{definition}
\textbf{Node Ambiguity:} In a heterogeneous network, The \emph{Ambiguity} of a node $V$ is the number of nodes that have the same network structure with $V$. We apply the entropy formula to compute this feature as:\\
\begin{equation}
-log \frac{1}{n}
\end{equation}
where \emph{n} is the number of nodes that are not only connect to the same neighbor set, but also have the same type with a specific node.
\end{definition}
Tack the Fig.~\ref{fig:ex2} for example, a query \emph{"A circle node that is connected with the node 1"} has $-log 0.5=0.3$ entropy; while the query \emph{"A circle node that is connected with the node 2"} has $-log 1=0$ entropy. We sum up all entropy values to represent the community ambiguity as:\\
\begin{definition}
\textbf{Community Ambiguity:} In a heterogeneous network, The \emph{Ambiguity} is the number of total entropy over all nodes in that community. More specifically, if we have \emph{k} nodes in a community, the total entropy can be computed as:\\
\begin{equation}
H(x)=-\sum_{i=1}^k log \frac{1}{n_i}
\end{equation}
\end{definition}
The lower the entropy, the higher distinguishable of this community. And, we have $\lim_{n_i\to1}H(x)=0$. The most important goal in this study is to have a community with a small value of H(x). If the H(x) value of a community is 0, we call it a uniquely identified community.\\
Despite we have a community with a small entropy, it is possible to achieve 0 entropy by include many nodes into the community. In fact, if we include all nodes, we can definitely have a 0-entropy community since all nodes can be identified with each other. However, this is unacceptable since such community is exactly equal to the original graph. Therefore, we need to have both low entropy and a small community size. In other words, we should achieve 0 entropy with as less nodes as possible. We have a formal definition to measure that how many nodes we need to uniquely identify each node in a community.\\
\begin{definition}
\textbf{Total Uniquely Identified Nodes (TUIN)} The TUIN is the sum of all number of nodes that are required to uniquely identify each node in the community. Suppose we have \emph{k} nodes in a community the \emph{TUIN} is computed as:\\
\begin{equation}
TUIN=\sum_{i=1}^k minIden(n_i)
\end{equation}
where $minIden(n_i)$ is the minimum number of nodes needed to uniquely identify the node $n_i$.
\end{definition}

\subsection{A Greedy Algorithm}

\subsection{n-hop(s) Algorithm}

\subsection{Ego-Centric Exploration Algorithm}

\subsection{Random Walk Algorithm}

\section{Evaluation}

\subsection{Data Sets}
Introducing our synthetic data sets and all 3 real data sets here.

%Table Formate
%\begin{table}[!t]
%\renewcommand{\arraystretch}{1.3}
%\caption{A Graph Database Example - Table \emph{Nodes}}
%\label{table:ex1-1}
%\centering
%\begin{tabular}{c||c}
%\hline
%\bfseries NodeID & \bfseries NodeType\\
%\hline\hline
%0 & C\\
%1 & S\\
%2 & S\\
%3 & C\\
%4 & C\\
%\hline
%\end{tabular}
%\end{table}

%\begin{table}[!t]
%\renewcommand{\arraystretch}{1.3}
%\caption{A Graph Database Example - Table \emph{Edges}}
%\label{table:ex1-2}
%\centering
%\begin{tabular}{c||c||c||c}
%\hline
%\bfseries SourceNodeID & \bfseries SourceNodeType & \bfseries DestNodeID & \bfseries DestNodeType \\
%\hline\hline
%0 & C & 1 & S \\
%0 & C & 2 & S \\
%1 & S & 3 & C \\
%1 & S & 4 & C \\
%\hline
%\end{tabular}
%\end{table}

\subsection{Synthetic Data Results}

\subsection{Real Data Results}

%\subsubsection{Subsubsection Heading Here}
%Subsubsection text here.


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%\subfloat[Case II]{\includegraphics[width=2.5in]{subfigcase2}%
%\label{fig_second_case}}}
%\caption{Simulation results}
%\label{fig_sim}
%\end{figure*}
%
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% An example of a floating table. Note that, for IEEE style tables, the
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%One & Two\\
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%Three & Four\\
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\section{Conclusion}
The conclusion goes here.

\section*{Acknowledgment}
The authors would like to thank...

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% references section

\bibliographystyle{IEEEtran}
\bibliography{EgoCommBib}

% that's all folks
\end{document}


